The marginal utilities of hamburgers and Cokes for a certain consumer are given as follows:

MU_H = C/H and MU_C = H/C

1. Show that the law of diminishing marginal utility applies to both goods.
2. If P_H = $4, P_{C =}$1, and consumer income is $18, determine the optimal levels of hamburgers and Cokes consumed.
3. If prices stay the same but income rises to $24, how is your answer to section b affected?Are hamburgers and Cokes normal or inferior goods? Explain.
4. If only the price of hamburger is lowered to $1, how is your answer to section b affected? Are hamburgers and Cokes complements or substitutes? Why?